Toshiba Satellite M40X not booting

I'm trying to fix a laptop that recently stopped working for no apparent reason.

The screen doesn't turn on. When I leave the battery in and press power, everything (minus the display) fires up, then there is a loud beep, then after a (very) long pause it repeats (over and over). When I remove the battery and just start it with the AC adapter it turns on then almost immediately shuts off. I've tried jiggling the power cord, that doesn't appear to be the problem...

I've tried following the manual but I get to the part where it says to try an external display which I'm unable to as I don't have the wire for it (nor a tv that supports such). The manual doesn't mention the beeping.